Chapter 4.3, Problem 40PPS

To determine

Whether the bones are parallel or not.

Answer to Problem 40PPS

The given two lines are parallel to each other.

Explanation of Solution

Given information:

Scientist excavating a dinosaur mapped the site on a coordinate plane.

One bone lies from $\left(-5,8\right)$ to $\left(10,-1\right)$ and a second bone lies from $\left(-10,-3\right)$ to $\left(-5,-6\right)$ are the bones parallel.

Calculation:

The slope of the line $m_1$ joining the points $R\left(-5,8\right)$ and $S\left(10,1\right)$

  $\begin{array}{c}{m}_1=\frac{-1-8}{10-\left(-5\right)}\\ =-\frac{9}{15}\\ =-\frac{3}{5}\end{array}$

The slope of the line $m_2$ joining the points $J\left(-10,-3\right)$ and $k\left(-5,-6\right)$

  $\begin{array}{c}{m}_2=\frac{-6-\left(-3\right)}{-5-\left(-10\right)}\\ =-\frac{3}{5}\end{array}$

Here $m_1=m_2$

Therefore, the given two lines are parallel to each other.